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29 Were lines drawn haphazard over the surface of a globe, the chances are ever so many to one against more than two lines crossing each other at any point. Simple crossings of two lines would of course be common in something like factorial proportion to the number of lines, but that any other line should contrive to cross at the same point would be a coincidence whose improbability only a mathematician can properly appreciate, so very great is it. If the lines were true lines, without breadth, the chances against such a coincidence would be infinite; and even had the lines some breadth, the chances would be enormous against a rendezvous. In other words, we might search in vain for a single instance of such encounter. On the surface of Mars, however, instead of searching in vain, we find the thing occurring passim; this a priori most improbable rendezvousing proving the rule, not the exception. Of the crossings that are best seen, almost all are meeting-places for more than two canals. To any one who had not seen the canals, it would at once occur that something of the same improbability might be fulfilled by cracks radiating from centres of explosion or fissure. But such a supposition is at once negatived by the uniform breadth of the lines, a uniformity impossible in cracks, whose very mode of production necessitates their being bigger at one end than the other. We see examples of what might result from such action in the cracks that radiate from Tycho, in the moon, or, as we now from Professor W. H. Pickering's observations, from the craterlets about it. These cracks bear no resemblance whatever to the lines on Mars. They look like cracks; the lines on Mars do not. Indeed, it te 22k a 22 a et te ta ee er ee is safe to say that the Martian lines would never so much as suggest cracks to any one. Lastly, the different radiations fit into one another absolutely, an utter impossibility were they radiating rifts from different centres. In the same way, we may, while we are about it, show that the lines cannot be several other things which they have, more or less gratuitously, been taken to be. They cannot, for example, be rivers; for rivers could not be so obligingly of the same size at source and mouth, nor would they run from preference on arcs of great circles. To do so, practically invariably, would imply a devotion to pure mathematics not common in rivers. They may, in some few instances, be rectified rivers, which is quite another matter. Glaciation cracks are equally out of the question: first, for the causes above mentioned touching cracks in general; and second, because there is, unfortunately, no ice where they occur. Nor can the lines be furrows ploughed by meteorites,--another ingenious suggestion,-- since in order to plough, invariably, a furrow from one centre to another, without either swerving from the course or overshooting the mark, the visitant meteorite would have to be carefully trained to the business. Such are the chief purely natural theories of the lines, excluding the idea of canals,-- theories advanced by persons who have not seen them. No one who has seen the lines well has or could advance them, inasmuch as they are not only disproved by consideration of the character of the lines, but instantly confuted by the mere look of alo them. Schiaparelli supposes the canals to be canals, but of geologic construction. He suggests, however, no explanation of how this is possible; so that the suggestion is not, properly